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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37441完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Hao-Chih Lee | en |
| dc.contributor.author | 李浩志 | zh_TW |
| dc.date.accessioned | 2021-06-13T15:28:16Z | - |
| dc.date.available | 2009-07-26 | |
| dc.date.copyright | 2008-07-26 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-16 | |
| dc.identifier.citation | [1] R. P. Araujo, D. L. S. McElwain, A history of the study of solid tumour growth: The contribution
of mathematical modelling ,66 (2004), Bull. Math. Biol., 10391091 [2] A. C. Burton, rate of growth of solid tumors as a problem of diffusion,30 (1966), Growth., Soc., 157-176 [3] H. Byrne and M. A. J. Chaplain,Growth of nonnecrotic tumors in the presence and absence of inhibitors, Math. Biosci. 130 (1995), 151-181. [4] H.M. Byrne, The role of mathematics in solid tumour growth, 35 (1999), Math. Today, 5989. [5] V. Cristini,J.S. Lowengrub, Q. Nie, Nonlinear simulation of tumor growth, J. Math. Biol., 46 (2003), 191-224. [6] A. Friedman, A hierarchy of cancer models and their mathematical challenges, Discrete and con- tinuous dynamical system, Vol. 4, series B, (2004), 147-159. [7] A. Friedman, F. Reitich, Symmetry-breaking bifurcation of analytic solutions to free boundary prob- lems: An application to a model of tumor growth, 353 (2001), Trans. Amer. Math., Soc., 1587-1634 [8] H.P. Greenspan, Models for the growth of a solid tumor by diffusion,52 (1972), Stud. Appl. Math.,317-340. [9] S. Gottlieb, C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comput. 67 (1998), 73 -85. [10] C. S. Hogea, B. T. Murray, J. A. sethian Simulation complex tumor dynamics from avascular to vascular growth using a general level-set method, J. Math. Biol., 53 (2006), 86-134. [11] R. J. LeVeque, Z. Li, The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources, SIAM J. Numer. Anal, 31 (1994), 1019-1044 [12] P. Macklin, J. Lowengrub Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth, J. Comput. Phys., 203 (2005), 191-220. [13] S. Osher, J. A. Sethian,, Front propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49. [14] S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surface, Springer, New york, NY, 2002, ISBN 0-387-95482-1. [15] S. Osher, C. H. Shu,High order essentially non-oscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), 907-922 [16] D. Peng, B. Merriman, S. Osher, H. K. Zhao, M. Kang, A PDE-based fast local level set method, J. Comput. Phys., 155, 1999, 410-438. [17] J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, New york, NY, 1999, ISBN 0-521-64557-3. [18] L. Zhang,C. A. Athale,T. S. Deisboeck, Development of a three-dimensional multiscale agent- based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. , J. Theor. Biol., 244(1) 2007, 96-107 [19] X. Zheng, S. M. Wise, V. Cristini, Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method 67 (2005),Bull. Math. Biol., pp. 211-259 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37441 | - |
| dc.description.abstract | 腫瘤生長的邊界演進是個不穩定的過程。在數值模擬中，介面的演進對於自身的曲率通常相當敏感，因而導致了不正確的計算與不穩定性。在這篇論文中，我們提出一個奠基在最小平方法上的邊界速度延拓方法，這個方法搭配上等位函數法（Level set method），可以成功模擬連續的腫瘤生長模型，並達到二階精確度。 | zh_TW |
| dc.description.abstract | The growth of
tumor boundary is an unstable evolution process. In numerical simulation, the evolution of the boundary is technically very sensitive to its curvature, and causes numerical instability and incorrect calculation. In this paper, we propose a least-square method for the extension of the boundary velocity. This extension, together with the level set method, can compute a continuous model for the tumor growth and achieve the second order accuracy. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T15:28:16Z (GMT). No. of bitstreams: 1 ntu-97-R95221008-1.pdf: 534653 bytes, checksum: 6bf6b154d202250d9809dbc90e522968 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Acknowledgements pi
Abstract (in Chinese) pii Abstract (in English) piii Contents piv Figures piv Tables piv 1. Introduction p1 1.1. Derivation of Governing Equations p1 1.2. A Model of Nonnecrotic Tumor p4 1.3. Dimensionless Formulation p5 1.4. Introduction to Level Set Method p6 2. Numerical Methods p8 2.1. Main Loop p8 2.2. Notations p8 3. Solving Poisson Equation on Arbitrary Domain p9 3.1. Discretize Poisson equation over arbitrary domain p9 3.2. Finding intersection of interface and grid lines p11 3.3. Curvature Discretization and Interpolation p12 4. Level Set p14 4.1. Numerical Flux p14 4.2. Spatial Discretization p14 4.3. Temporal Discretization p16 4.4. Redistancing p16 4.5. Normal Vector p17 5. Treatment in Computing Velocity p18 5.1. Discretization of Prevelocity p18 5.2. Least Square Velocity Extension p19 5.3. Velocity Filtering p21 6. Numerical Results p23 6.1. Poisson Solver p23 6.2. Interface Propagator and Velocity Related 28 6.3. Overall Method p32 7. Conclusion p37 8. Appendix p38 References p39 | |
| dc.language.iso | en | |
| dc.subject | 界面問題 | zh_TW |
| dc.subject | 等位函數法 | zh_TW |
| dc.subject | 腫瘤生長 | zh_TW |
| dc.subject | 最小平方 | zh_TW |
| dc.subject | 速度場延拓 | zh_TW |
| dc.subject | least square | en |
| dc.subject | interface evolution | en |
| dc.subject | velocity extension | en |
| dc.subject | tumor growth | en |
| dc.subject | level set | en |
| dc.title | 速度場最小平方延拓的界面演進法：應用在腫瘤生長模擬 | zh_TW |
| dc.title | Interface Evolution via a
Least-Square Velocity Extension: Application to Tumor Growth | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張建成(Chien-Cheng Chang),許文翰(Wen- Hann Sheu) | |
| dc.subject.keyword | 腫瘤生長,等位函數法,最小平方,速度場延拓,界面問題, | zh_TW |
| dc.subject.keyword | tumor growth,level set,least square,velocity extension,interface evolution, | en |
| dc.relation.page | 40 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-17 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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